military W2 shows wage from state (non SLR)

Taxpayer graduated from college in 2020 and joined National Guard stationed in CT. His state of legal residence is NJ.
In his w2, however, state wage from CT is listed but not NJ.
Should he have the w2 corrected?
Any other options?
Thank you!

Was CT his home of record when he enlisted?
SLR can be changed, HOR can't.

Personnel whose home of record is Connecticut
If your home of record is Connecticut you are a resident of Connecticut. As a resident you must file a resident return and pay any tax due unless you meet all of the following conditions for the entire taxable year:
You did not maintain a permanent place of abode in Connecticut;
You maintained a permanent place of abode outside Connecticut; and
You spent 30 days or less in Connecticut.
If you meet all three conditions, you are considered a nonresident of Connecticut for the taxable year.

Was CT his home of record when he enlisted?
SLR can be changed, HOR can't.

Personnel whose home of record is Connecticut
If your home of record is Connecticut you are a resident of Connecticut. As a resident you must file a resident return and pay any tax due unless you meet all of the following conditions for the entire taxable year:
You did not maintain a permanent place of abode in Connecticut;
You maintained a permanent place of abode outside Connecticut; and
You spent 30 days or less in Connecticut.
If you meet all three conditions, you are considered a nonresident of Connecticut for the taxable year.

Thank you for the help!
He jointed the Army in CT but he has been a resident of NJ all the time. Is his home of record CT or NJ? Based on my understanding, it should be CT even he was not CT resident when he joined army from there, right?

HOR is CT.
SLR is NJ.

Withholding: If your home of record is Connecticut but you meet all three criteria above for being considered a nonresident (or you meet the Group B exception described in IP 2019(5) you are not subject to tax on your military pay. However, DFAS will withhold Connecticut income tax unless you complete Form CT-W4 each year and enter "E" on Line 1 to claim exemption from the tax. Unless you provide a new Form CT-W4 to your paymaster each year by February 15, the paymaster will begin to withhold Connecticut income tax for that year.

HOR is CT.
SLR is NJ.

Withholding: If your home of record is Connecticut but you meet all three criteria above for being considered a nonresident (or you meet the Group B exception described in IP 2019(5) you are not subject to tax on your military pay. However, DFAS will withhold Connecticut income tax unless you complete Form CT-W4 each year and enter "E" on Line 1 to claim exemption from the tax. Unless you provide a new Form CT-W4 to your paymaster each year by February 15, the paymaster will begin to withhold Connecticut income tax for that year.

Thanks for the help!
As his home of record is CT and he stayed there more than 30 days, he is treated as CT resident. So, he will need to file resident returns for both CT and NJ? Will he get credit for tax paid to CT on his NJ resident return?
Thanks.